Average Error: 5.8 → 0.1
Time: 8.8s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[1 \cdot x + \left(x \cdot y\right) \cdot y\]
x \cdot \left(1 + y \cdot y\right)
↓
1 \cdot x + \left(x \cdot y\right) \cdot y
double f(double x, double y) {
        double r582757 = x;
        double r582758 = 1.0;
        double r582759 = y;
        double r582760 = r582759 * r582759;
        double r582761 = r582758 + r582760;
        double r582762 = r582757 * r582761;
        return r582762;
}
↓
double f(double x, double y) {
        double r582763 = 1.0;
        double r582764 = x;
        double r582765 = r582763 * r582764;
        double r582766 = y;
        double r582767 = r582764 * r582766;
        double r582768 = r582767 * r582766;
        double r582769 = r582765 + r582768;
        return r582769;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.8

    \[x \cdot \left(1 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in5.8

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]

  4. Simplified5.8

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot \left(y \cdot y\right)\]
  5. Using strategy rm

  6. Applied associate-*r*0.1

    \[\leadsto 1 \cdot x + \color{blue}{\left(x \cdot y\right) \cdot y}\]

  7. Final simplification0.1

    \[\leadsto 1 \cdot x + \left(x \cdot y\right) \cdot y\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1 (* y y))))